Theorem mulcomi 8322

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
mulcomi	|- ( A x. B ) = ( B x. A )

Proof of Theorem mulcomi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcom 8298	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )
4	1, 2, 3	mp2an 430	1 |- ( A x. B ) = ( B x. A )

Syntax hints:   = wceq 1402   e. wcel 2209  (class class class)co 6075   CCcc 8167   x. cmul 8174

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-mulcom 8270

This theorem is referenced by:  mulcomli  8323  8th4div3  9503  numma2c  9801  nummul2c  9805  9t11e99  9885  binom2i  11063  fac3  11148  tanval2ap  12458  pockthi  13115  decsplit1  13185  decsplit  13186  sincosq4sgn  15853  2logb9irrALT  15999  2lgsoddprmlem2  16139  2lgsoddprmlem3d  16143